Auxiliary Variable-Aided Hybrid Message Passing for Joint Channel, Phase Noise Estimation and Detection for Multi-User MIMO Systems

Abstract

This paper considers a multi-user multiple-input multiple-output (MU-MIMO) system with independent phase noise (PN) at user terminals (UTs) due to non-synchronous noisy local oscillators. The conventional factor graph of MU-MIMO involves an observation factor with multiple high-dimensional variables in the form of multiplication and summation. In this work, the MU-MIMO factor graph is represented by introducing auxiliary variables, which enables the decomposition of the observation factor into several simpler sub-factors and then use different message passing techniques to obtain approximate marginals. Specifically, belief propagation and expectation propagation (BP-EP) are used for the linear factors for random walk process, modulation and coding, while mean field (MF) is used for non-linear factor in exponential form. To reduce the computational complexity, the non-Gaussian MF messages are approximated to be Gaussian by using the second order Taylor expansion at its belief obtained in the previous iteration. The proposed receiver has a quadratic computational complexity per symbol per iteration. Simulation results show that the performance of the proposed receiver is better than existing methods and is close to the matched filter bound (MFB) in terms of the bit error rate (BER).